To find the magnitude of the dilation from polygon ABCD to polygon A'B'C'D', we look at corresponding points. The dilation factor can be determined by selecting corresponding points and calculating the ratio of the distances from the origin (0,0).
For example, if a point \( (x,y) \) on polygon ABCD maps to point \( (kx, ky) \) on polygon A'B'C'D', the dilation factor \( k \) would be calculated as follows:
- Measure the distance from the origin to a point on ABCD (let's choose point \( A \) as \( (x_1, y_1) \)).
- Measure the distance from the origin to the corresponding point on A'B'C'D' (let's say point \( A' \) is at \( (kx_1, ky_1) \)).
- Compute the ratio \( k = \frac{\text{Distance to A'}}{\text{Distance to A}} \).
The values in the provided options are 1, 3, \( \frac{1}{2} \), and 2. You need to calculate or simply observe a ratio that corresponds with one of these values based on the graphical representation of ABCD and A'B'C'D'.
Without the actual image or specific coordinates, I recommend examining the distances visually or using the coordinates if provided to calculate \( k \).
If you determine that the dilation from polygon ABCD to polygon A'B'C'D' reduces or increases the size of the shape by a specific factor, you would select that option. For instance, if points distance from the origin doubles, then the dilation factor is 2. If it reduces to half the size, the dilation factor is \( \frac{1}{2} \).
Please calculate to ascertain the correct magnitude of the dilation. If unsure, you can frequently assume that simple whole number values (like 1, 2, or 3) are common dilation factors in straightforward problems.
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